Which Graph Shows A Dilation

What is a Dilation?

A dilation is a type of transformation that changes the size of the prototype. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a film of each type of dilation (one that gets larger and ane that gest smaller).

Example 1

The picture below shows a dilation with a scale factor of 2. This ways that the image, A', is twice as large as the pre-image A. Like other transformations, prime number notation is used to distinguish the paradigm fromthe pre-epitome. The image always has a prime after the letter such equally A'.

$Picture of a dilation in math$

Example 2

Dilations can also reduce the size of shape. The picture below demonstrations a dilation of $$ \frac{1}{2}$$ Any time that the scale gene is a fraction, the image will get smaller.

Formula for Dilations

Information technology's always easier to understand a concept by looking at specific examples with pictures, so I suggest looking at the dilation examples below showtime...earlier you lot try to internalize the steps listed below and that explain the general formula for dilating a betoken with coordinates of (2, 4) by a scale factor of $$\carmine { \frac 1 2 }$$.

ane) Multiply both coordiantes by scale factor	($$two \cdot \red { \frac one ii } ,4 \cdot \red { \frac 1 2 }$$)
two) Simplify	(one, 2)
3) Graph (if required)

Demonstration of Dilation, Calibration factor of three

animation of a dilation

Practice Problems

Problem 1

Perform a Dilation of 3 on point A (2, 1) which you tin see in the graph below.

Multiply the coordinates of the original bespeak (ii, i), called the image, by iii.

Epitome'due south coordinates = (2 * three, i * 3) to become the coordinates of the image (6, 3).

Problem 2

Perform a Dilation of 4 on signal A (2, 3) which y'all can see in the flick below.

Multiply the coordinates of the original indicate (2, 3), chosen the prototype, by four.

Image's coordinates = (2 * 4, 3 * 4) to get the coordinates of the image (8, 12).

Problem three

Perform a Dilation of ½ on point A (2, 4) which you can see in the picture below.

Use the formula for dilations.

1) Multiply both coordiantes past scale gene	(2 * ½, four * ½)
2) Simplify	(1, 2)
three) Graph (if required)	run into motion picture below

Problem 4

Perform a Dilation of 1/3 on indicate A (3, 6) which y'all can see in the movie below.

Use the formula for dilations.

one) Multiply both coordiantes by scale gene	(3 * one/3, 6 * 1/3)
two) Simplify	(1,2)
3) Graph(if required)	meet film below

Problem 5

What is the image of Triangle ABC graphed below after a dilation of ½?

dilation picture

Multiply each vertex by the scale factor of ½! And plot the new coordinates.